Canadian Mathematics Competition An activity of the Centre for Education in Mathematics and Computing, University of Waterloo, Waterloo, Ontario Concours canadien de math´ ematiques Une activit´ e du Centre d’´ education en math´ ematiques et en informatique, Universit´ e de Waterloo, Waterloo, Ontario 2009 Results Pascal Contest (Grade 9) Cayley Contest (Grade 10) Fermat Contest (Grade 11) 2009 R´ esultats Concours Pascal (9 e ann´ ee – Sec. III) Concours Cayley (10 e ann´ ee – Sec. IV) Concours Fermat (11 e ann´ ee – Sec. V) Avec la contribution de: Avec la participation de: c 2009 Centre for Education in Mathematics and Computing
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2009 Pascal Contest Concours Pascal - CEMCJASMINE ZHANG Bayview S.S. Richmond Hill 10 DONG CHENZHOU E.S. St. Luc Montreal 10 ANANDA ZHU John Fraser S.S. Mississauga 10 TEAMS / EQUIPES´
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CanadianMathematicsCompetition
An activity of the Centre forEducation in Mathematics and Computing,University of Waterloo, Waterloo, Ontario
Concourscanadien demathematiquesUne activite du Centre d’educationen mathematiques et en informatique,Universite de Waterloo, Waterloo, Ontario
2009Results
Pascal Contest(Grade 9)
Cayley Contest(Grade 10)
Fermat Contest(Grade 11)
2009Resultats
Concours Pascal(9e annee – Sec. III)
Concours Cayley(10e annee – Sec. IV)
Concours Fermat(11e annee – Sec. V)
Avec la contribution de: Avec la participation de:
Wally Webster (Chair / president), Dashwood, ONLloyd Auckland, St. Thomas, ONJanet Christ, Walter Murray C.I., Saskatoon, SKNerissa Coronel, St. Marguerite d’Youville C.S.S., Brampton, ONJP Pretti, University of Waterloo, Waterloo, ONJim Schurter, University of Waterloo, Waterloo, ONTyler Somer, Kitchener, ONAnna Spanik, Halifax West H.S., Halifax, NS
Cayley Contest / Concours Cayley
Jeff Anderson (Chair / president), Forest Heights C.I., Kitchener, ONTom Barker, Stratford, ONSteve Furino, University of Waterloo, Waterloo, ONShawn Godin, Cairine Wilson S.S., Orleans, ONCatherine Haines, Toronto, ONChristopher Ing, Vincent Massey S.S., Windsor, ONJack Koenka, Toronto, ONJen Nissen, University of Waterloo, Waterloo, ON
Fermat Contest / Concours Fermat
Paul Fennell (Chair / president), London, ONFiona Dunbar, University of Waterloo, Waterloo, ONSteve Lau, John Diefenbaker S.S., Hanover, ONCliff Lelievre, Oakville, ONDean Murray, University of Waterloo, Waterloo, ONAlexandru Pintilie, Crescent School, Toronto, ONDan Schnabel, Vaughan S.S., Thornhill, ONDavid Shepherd, Ravenna, ON
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Foreword Avant-Propos
The Centre for Education in Mathematics and Computing is proud to once again be the major sponsor of theCanadian Mathematics Competition this year. The year 2009 marks the 47th year of Contests produced by theCanadian Mathematics Competition.
Our congratulations go to all who participated in this year’s Pascal, Cayley and Fermat Contests. This year’sContests were resounding successes, with average of 87.9, 90.0 and 85.1 across the three Contests. The number ofstudents with perfect papers on the three Contests were 5, 19 and 3. We are very pleased with these results. Theoverall number of students writing this year’s papers showed a small increase over that from 2008.
Again this year, individual school results were available online in “real time” as we scanned and marked forms.As a result, we were able to have some students’ scores available within two days of the Contests. We hope thatit is helpful to you to get such quick feedback.
As always, we would like to thank the hard-working Problems Committees. Most of the members of these Com-mittees are active secondary school teachers from across Canada who volunteers their time and contribute dozensof hours of expertise. Without their intriguing and sometimes amusing problems, these Contests would not bepossible.
We would also like to thank all participants, both teachers and students. We hope that the papers providedyou with some interesting mathematics to think about and play with. Thank you for your support! Please con-tinue to encourage your colleagues and fellow students to become involved in our activities.
Le Centre d’education en mathematiques et en informatique a encore une fois le plaisir d’etre un majeur sup-porter du Concours canadien de mathematiques. L’annee 2009 marque la 47e annee de concours produit par leConcours canadien de mathematiques.
Nos felicitations vont a tous les participants du Concours Pascal, Cayley et Fermat de cette annee. Les Con-cours de cette annee retentissaient de succes, avec des moyennes de 87,9, 90,0 et 85,1 a travers les trois Concours.Le nombre d’etudiants possedant un concours parfait etait de 5, 19 et 3. Nous sommes satisfait de ces resultats.L’ensemble du nombre de participants cette annee a montre une petite augmentation comparee a 2008.
Encore une fois cette annee, les resultats d’ecole etaient disponible en ligne au fur et a mesure que nous avionsbalaye et corrige les formulaires de reponses. Par consequent, nous avions les resultats pour beaucoup des etudiantsdisponibles deux jours apres les Concours. Nous esperons qu’il vous est utile de recevoir des resultats aussi rapi-dement.
Nous aimerions surtout remercier les Comites de problemes pour leur dur travail. La plupart des membres de cesComites sont des enseignant(e)s d’ecole secondaire actifs d’un bout a l’autre du Canada qui offre leur temps etcontribuent des douzaines d’heures d’expertise. Sans leurs problemes perspicaces et amusants, ces Concours neseraient pas possibles.
Nous aimerions remercier aussi tous les participants incluant les enseignants et les etudiants. Nous esperonsque les concours vous ont offert des mathematiques interessantes qui vous ont amusees et portees a reflechir.Merci pour votre soutien continue!
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Enrollment Inscription
Number of schools registered by province /Nombre d’ecoles inscrit par province
Total number of students enrolled / Nombre d’inscriptions individuelles: 84466
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Champions – 2009 Champions – 2009
2009 STUDENT CHAMPIONS AND CHAMPIONSHIP TEAMSPALMARES INDIVIDUEL ET PALMARES PAR EQUIPE 2009
PASCAL CONTEST / CONCOURS PASCAL
STUDENTS /ELEVESStudents are listed in alphabetical order / Les eleves sont nommes en ordre alphabetique
Gold Medals School Location GradeMedailles d’or Ecole Endroit NiveauANQI DONG Walter Murray C.I. Saskatoon 9ANDY LI Moscrop S.S. Burnaby 9MATHIEU NASSIF College Jean de Brebeuf Montreal 9COLIN TA Windermere S.S. Vancouver 9HENG TANG Bayview S.S. Richmond Hill 9
TEAMS / EQUIPES
School Location ScoreEcole Endroit Note
Champion / Premiere University of Toronto Schools Toronto 427Second / Deuxieme College Jean de Brebeuf Montreal 424Third / Troisieme Walter Murray C.I. Saskatoon 422Fourth / Quatrieme Glenforest S.S. Mississauga 421Fifth / Cinquieme Colonel By S.S. Gloucester 420
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Champions – 2009 Champions – 2009
2009 STUDENT CHAMPIONS AND CHAMPIONSHIP TEAMSPALMARES INDIVIDUEL ET PALMARES PAR EQUIPE 2009
CAYLEY CONTEST / CONCOURS CAYLEY
STUDENTS /ELEVESStudents are listed in alphabetical order / Les eleves sont nommes en ordre alphabetique
Gold Medals School Location GradeMedailles d’or Ecole Endroit NiveauJOSEPH ALACCHI Loyola H.S. Montreal 10KEVIN CHU Moscrop S.S. Burnaby 10JAY DOU Moira S.S. Belleville 10JIMMY FANG St. Robert C.H.S. Thornhill 10AILEEN GAO Sir Winston Churchill S.S. Vancouver 10LINCOLN GUO University of Toronto Schools Toronto 9SHANE HU Marc Garneau C.I. North York 10LEO LAI Point Grey S.S. Vancouver 8TIAN LAN Northern S.S. Toronto 10ELLEN LEE St. Francis Xavier S.S. Mississauga 10XIN NING A.Y. Jackson S.S. North York 10KRISS PETROUNOV Marc Garneau C.I. North York 10SIMON YOUNAN St. Francis Xavier S.S. Mississauga 10STEVEN YU Pinetree S.S. Coquitlam 9JOE ZENG Don Mills C.I. North York 10ERIC ZHAN University of Toronto Schools Toronto 9JASMINE ZHANG Bayview S.S. Richmond Hill 10DONG CHENZHOU E.S. St. Luc Montreal 10ANANDA ZHU John Fraser S.S. Mississauga 10
TEAMS / EQUIPES
School Location ScoreEcole Endroit Note
Champion / Premiere Marc Garneau C.I. North York 444Second / Deuxieme University of Toronto Schools Toronto 442Third / Troisieme Don Mills C.I. North York 436
Northern S.S. Toronto 436Fifth / Cinquieme E.S. St. Luc Montreal 434
Sir Winston Churchill S.S. Vancouver 434
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Champions – 2009 Champions – 2009
2009 STUDENT CHAMPIONS AND CHAMPIONSHIP TEAMSPALMARES INDIVIDUEL ET PALMARES PAR EQUIPE 2009
FERMAT CONTEST / CONCOURS FERMAT
STUDENTS /ELEVESStudents are listed in alphabetical order / Les eleves sont nommes en ordre alphabetique
Gold Medals School Location GradeMedailles d’or Ecole Endroit NiveauLIZ CHEN Walter Murray C.I. Saskatoon 11ROBIN CHENG Pinetree S.S. Coquitlam 11JAMES LAM E.S. Antoine Brossard Brossard 11JAMES RICKARDS Colonel By S.S. Gloucester 9MARIYA SARDARLI McKernan J.H.S. Edmonton 9
TEAMS / EQUIPES
School Location ScoreEcole Endroit Note
Champion / Premiere Pinetree S.S. Coquitlam 425Second / Deuxieme University of Toronto Schools Toronto 422Third / Troisieme Don Mills C.I. North York 416Fourth / Quatrieme Earl Haig S.S. North York 414
Richmond Hill H.S. Richmond Hill 414
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Champions – 2009 Champions – 2009
2009 FERMAT CONTEST PROVINCIAL CHAMPIONSCHAMPIONS PROVINCIAUX AU CONCOURS FERMAT 2009
Each student below will receive a $200 prize / Chaque etudiant ci-dessous recevrait un prix de 200 $
Province Student School LocationProvince Etudiant Ecole EndroitNL JORDAN ANSTEY New World Island Academy SummerfordNS CASPER MACAULAY Halifax Grammar School HalifaxNB XI ZHANG Saint John H.S. Saint JohnPE MICHAEL LI Colonel Gray Sr. H.S CharlottetownQC JAMES LAM E.S. Antoine Brossard BrossardON North WILL HALL Banting Memorial H.S. AllistonON North MATTHEW HYNDMAN Central Algoma S.S. DesbaratsON East JAMES RICKARDS Colonel By S.S. GloucesterON Metro BRIAN BI Woburn C.I. ScarboroughON Metro DENNIS LU Earl Haig S.S. North YorkON West LOUIS HONG Sir John A. Macdonald S.S. WaterlooON West CHEN SUN A.B. Lucas S.S. LondonON Central STEVEN YANG Rick Hansen S.S. MississaugaON Central DANIEL YOO Thornhill S.S. ThornhillMB GIUSEPPE GRANDE Grant Park H.S. WinnipegSK LIZ CHEN Walter Murray C.I. SaskatoonAB MARIYA SARDARLI McKernan J.H.S. EdmontonBC ROBIN CHENG Pinetree S.S. Coquitlam
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Correct Answers Bonnes Rponses
# Pascal Cayley Fermat1 D A D2 E E E3 D C C4 A D B5 D A A6 A D A7 C E D8 D B C9 B D C
10 C A E11 E C D12 D C C13 A E A14 A D E15 B A B16 E B C17 B C B18 D B B19 C D A20 E B A21 C E D22 E E E23 B A D24 B B D25 D C C
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Pascal Contest Concours Pascal
Number of Contestants / Nombre de concurrents: 27633Average mark / Note moyenne: 87.89
Percentage of contestants selecting each option / Pourcentage de concurrents par choix:
Correct % not % correctAnswer/ attempted/ of attemptedBonne % sans % tentatives
Reponse reponse reussies# A B C D E1 D 0.79 16.18 0.38 82.04 0.32 0.26 82.252 E 0.03 0.32 0.33 0.31 98.93 0.04 98.973 D 0.09 0.25 1.50 93.19 4.76 0.17 93.354 A 97.57 0.30 1.15 0.52 0.19 0.24 97.805 D 8.37 4.07 2.85 75.69 1.49 7.49 81.826 A 69.24 5.81 21.06 1.64 1.66 0.55 69.637 C 11.31 1.22 75.89 1.89 5.52 4.14 79.178 D 1.91 3.74 4.55 87.60 1.46 0.71 88.229 B 2.00 39.58 15.08 15.88 17.60 9.83 43.89
10 C 0.63 0.44 95.00 2.35 0.67 0.88 95.8411 E 20.77 9.22 4.43 8.21 53.25 4.09 55.5212 D 1.49 2.46 1.55 89.85 2.78 1.83 91.5313 A 76.43 2.36 3.39 6.69 3.47 7.61 82.7314 A 47.99 10.88 5.27 9.35 6.66 19.82 59.8515 B 19.57 40.77 8.90 6.37 7.74 16.62 48.8916 E 8.02 6.93 10.22 7.24 53.99 13.56 62.4617 B 7.42 42.85 6.54 8.24 6.66 28.26 59.7318 D 4.07 3.97 7.73 75.61 5.72 2.86 77.8319 C 6.10 8.91 39.48 12.04 15.33 18.11 48.2120 E 5.86 7.17 9.41 5.02 32.24 40.27 53.9721 C 11.92 4.91 28.08 17.93 21.49 15.64 33.2822 E 12.12 9.79 11.16 7.16 26.25 33.47 39.4723 B 8.99 9.54 30.07 9.26 4.59 37.52 15.2724 B 6.40 10.57 8.75 8.40 12.05 53.80 22.8725 D 7.07 9.33 9.36 6.89 7.62 59.69 17.10
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Cayley Contest Concours Cayley
Number of Contestants / Nombre de concurrents: 20958Average mark / Note moyenne: 90.00
Percentage of contestants selecting each option / Pourcentage de concurrents par choix:
Correct % not % correctAnswer/ attempted/ of attemptedBonne % sans % tentatives
Reponse reponse reussies# A B C D E1 A 98.18 1.15 0.07 0.10 0.25 0.18 98.362 E 0.05 0.34 0.27 0.24 98.99 0.05 99.043 C 0.24 0.18 95.05 1.44 2.80 0.23 95.274 D 2.72 1.18 1.22 93.38 0.12 1.32 94.635 A 88.33 11.00 0.17 0.14 0.07 0.23 88.546 D 5.36 3.33 4.78 79.70 0.67 6.10 84.887 E 3.41 9.04 4.63 1.29 75.75 5.83 80.448 B 4.60 72.59 5.66 10.38 1.45 5.27 76.639 D 0.87 1.59 1.04 93.42 2.00 1.02 94.38
10 A 78.17 4.16 3.12 4.30 4.70 5.50 82.7211 C 1.20 4.70 75.44 12.04 2.50 4.07 78.6412 C 0.52 2.91 93.89 1.70 0.47 0.46 94.3213 E 3.80 1.76 2.33 1.30 88.79 1.96 90.5714 D 5.10 8.75 8.67 51.93 11.56 13.93 60.3315 A 59.11 10.16 6.39 10.88 3.21 10.19 65.8216 B 1.70 38.59 2.61 19.62 20.90 16.53 46.2317 C 9.17 17.24 34.82 7.68 4.94 26.10 47.1218 B 11.83 34.32 9.28 3.81 6.47 34.24 52.1819 D 4.46 10.38 9.68 19.49 7.14 48.79 38.0520 B 14.37 28.63 8.08 6.71 6.17 35.97 44.7221 E 4.56 5.95 9.05 16.72 16.80 46.87 31.6222 E 5.45 4.27 11.52 16.53 20.25 41.92 34.8723 A 14.57 7.39 30.68 5.04 4.07 38.20 23.5724 B 10.01 9.87 8.89 14.11 6.71 50.36 19.8825 C 5.36 6.52 7.78 5.49 3.51 71.28 27.08
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Fermat Contest Concours Fermat
Number of Contestants / Nombre de concurrents: 17792Average mark / Note moyenne: 85.10
Percentage of contestants selecting each option / Pourcentage de concurrents par choix:
Correct % not % correctAnswer/ attempted/ of attemptedBonne % sans % tentatives
Reponse reponse reussies# A B C D E1 D 9.98 0.09 0.08 89.70 0.11 0.02 89.722 E 0.68 0.13 0.95 0.09 98.07 0.06 98.123 C 0.65 3.76 92.24 2.07 0.38 0.87 93.054 B 1.07 92.54 1.14 3.01 0.64 1.58 94.025 A 83.37 9.46 2.44 1.55 1.50 1.65 84.766 A 93.29 1.79 2.81 0.58 0.88 0.62 93.887 D 1.33 8.16 6.54 80.96 2.40 0.58 81.438 C 0.75 3.93 80.01 9.70 2.06 3.53 82.949 C 1.41 2.07 52.56 18.04 13.57 12.33 59.95
10 E 11.40 3.94 2.24 2.16 73.50 6.73 78.8111 D 0.61 0.39 15.82 72.54 7.80 2.82 74.6512 C 2.84 18.68 44.68 11.34 7.50 14.94 52.5313 A 26.85 5.48 21.23 16.33 14.13 15.96 31.9514 E 4.15 3.92 7.62 3.86 53.53 26.89 73.2215 B 8.52 66.38 14.33 5.41 1.41 3.92 69.0916 C 6.90 17.85 41.81 7.02 4.46 21.95 53.5617 B 11.69 28.01 11.07 6.51 4.99 37.70 44.9718 B 12.91 37.13 6.24 5.11 4.43 34.16 56.3919 A 66.78 2.80 4.34 3.05 4.47 18.53 81.9720 A 15.61 18.29 9.02 7.46 4.58 45.03 28.3921 D 7.75 7.78 28.12 26.65 6.40 23.26 34.7322 E 4.78 8.76 5.64 11.56 12.75 56.49 29.3023 D 2.51 5.91 11.61 19.12 4.41 56.42 43.8624 D 5.16 7.46 8.20 5.14 4.90 69.12 16.6425 C 4.74 10.49 7.82 4.86 4.15 67.91 24.38
Number of three student teams / Nombre d’equipes de trois elevesPascal Contest / Concours Pascal : 1049Cayley Contest / Concours Cayley : 966Fermat Contest / Concours Fermat : 958
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CanadianMathematicsCompetition
An activity of the Centre forEducation in Mathematics and Computing,University of Waterloo, Waterloo, Ontario
Concourscanadien demathematiquesUne activite du Centre d’educationen mathematiques et en informatique,Universite de Waterloo, Waterloo, Ontario
2009Results
Pascal Contest(Grade 9)
Cayley Contest(Grade 10)
Fermat Contest(Grade 11)
2009Resultats
Concours Pascal(9e annee – Sec. III)
Concours Cayley(10e annee – Sec. IV)
Concours Fermat(11e annee – Sec. V)
Cayley Contest Honour RollsPalmares pour le concours Cayley
Score/NoteCity/VilleRank/Rang
School/École
444North York1 Marc Garneau C.I.
442Toronto2 University of Toronto Schools
436North York3 Don Mills C.I.
436Toronto3 Northern S.S.
434Montreal5 E.S. St. Luc
434Vancouver5 Sir Winston Churchill S.S.
432Mississauga7 St. Francis Xavier S.S.
430Coquitlam8 Pinetree S.S.
430Edmonton8 Old Scona Academic H.S.
430North York8 A.Y. Jackson S.S.
428Windsor11 Vincent Massey S.S.
426Vancouver12 University Transition Program
426North York12 Earl Haig S.S.
424Calgary14 Sir Winston Churchill H.S.
424West Vancouver14 West Vancouver S.S.
424Vancouver14 Lord Byng S.S.
424Thornhill14 St. Robert C.H.S.
422Richmond18 Richmond S.S.
422Richmond Hill18 Bayview S.S.
420Scarborough20 Dr. Norman Bethune C.I.
420Vancouver20 St. George's School
420Burnaby20 Burnaby North S.S.
420Richmond20 Hugh McRoberts S.S.
416Calgary24 Western Canada H.S.
414Surrey25 Semiahmoo S.S.
412Greenfield Park26 Centennial Reg. H.S.
412North York26 Crescent School
412Port Moody26 Port Moody Sr. S.S.
412Vancouver26 Point Grey S.S.
412Ottawa26 Lisgar C.I.
411Burnaby31 Moscrop S.S.
411North York31 Victoria Park C.I.
410Markham33 Markham D.H.S.
408Toronto34 North Toronto C.I.
407Vancouver35 Prince Of Wales Mini School
406Vancouver36 St. John's School
406North Vancouver36 Handsworth S.S.
404Montreal38 College Jean de Brebeuf
403Richmond Hill39 Richmond Hill H.S.
402Scarborough40 Agincourt C.I.
402Waterloo40 Waterloo C.I.
402Vancouver40 University Hill S.S.
402Mississauga40 The Woodlands School
402Nepean40 Bell H.S.
402Vancouver40 Crofton House School
400Delta46 Seaquam S.S.
400Mississauga46 Glenforest S.S.
400Hamilton46 Westdale S.S.
400Coquitlam46 Gleneagle S.S.
400North York46 York Mills C.I.
398Burnaby51 Burnaby South S.S.
398London51 A.B. Lucas S.S.
2009Cayley Contest/Concours Cayley
Team List/Palmarès d'équipes
Grade/NiveauLocation/Endroit
Name/Nom School/École
Group I/Groupe I Scores/Notes 150 - 145ALACCHI JOSEPH 10MontrealLoyola H.S.
CHU KEVIN 10BurnabyMoscrop S.S.
DOU JAY 10BellevilleMoira S.S.
FANG JIMMY 10ThornhillSt. Robert C.H.S.
GAO AILEEN 10VancouverSir Winston Churchill S.S.
GUO LINCOLN 9TorontoUniversity of Toronto Schools
HU SHANE 10North YorkMarc Garneau C.I.
LAI LEO 8VancouverPoint Grey S.S.
LAN TIAN 10TorontoNorthern S.S.
LEE ELLEN 10MississaugaSt. Francis Xavier S.S.
NING XIN 10North YorkA.Y. Jackson S.S.
PETROUNOV KRISS 10North YorkMarc Garneau C.I.
YOUNAN SIMON 10MississaugaSt. Francis Xavier S.S.
YU STEVEN 9CoquitlamPinetree S.S.
ZENG JOE 10North YorkDon Mills C.I.
ZHAN ERIC 9TorontoUniversity of Toronto Schools
ZHANG JASMINE 10Richmond HillBayview S.S.
ZHOU DONG CHEN 10MontrealE.S. St. Luc
ZHU ANANDA 10MississaugaJohn Fraser S.S.
Group II/Groupe II Scores/Notes 144 - 143VancouverUniversity Transition ProgramCHEN PENGHONG 10